Existence of weak solutions for unsteady motions of micro-polar electrorheological fluids

TL;DR

This paper proves the existence of weak solutions for the unsteady motion equations of micro-polar electrorheological fluids with generalized Newtonian stress tensors, using advanced truncation techniques.

Contribution

It establishes the global existence of solutions for shear exponents greater than 6/5 in three-dimensional settings, extending previous results.

Findings

Existence of weak solutions for shear exponents p>6/5

Application of Lipschitz truncation methods

Global solutions in three-dimensional domains

Abstract

In this paper we study the existence of weak solutions to an unsteady system describing the motion of micro-polar electrorheological fluids. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. Using the Lipschitz truncation and the solenoidal Lipschitz truncation we establish the existence of global solutions for shear exponents $p>6/5$ in three-dimensional domains.